CN112200445B - Method for evaluating protective effect of grouting ring of newly-built tunnel on existing shield tunnel - Google Patents
Method for evaluating protective effect of grouting ring of newly-built tunnel on existing shield tunnel Download PDFInfo
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Abstract
The invention discloses a method for evaluating the protection effect of a grouting ring of a newly-built tunnel on an existing shield tunnel, which comprises the following steps: establishing a three-dimensional coordinate system and a grouting ring mechanical calculation model according to the relative positions of the newly-built tunnel, the existing tunnel and the grouting ring; according to the established mechanical model of the grouting ring, the influence process on the surrounding soil layer is simulated through the volume expansion of the grouting ring, and the random medium theory is utilized to deduce a solving formula of the additional stress of the surrounding soil layer caused by the expansion of the grouting ring; considering the influence of the excavation of the newly-built tunnel and the volume expansion of the grouting ring, and calculating the total vertical additional stress at the axis of the existing tunnel under the combined action of the excavation and the grouting ring; the vertical displacement of the existing tunnel can be obtained by substituting the total vertical additional stress into the shearing dislocation and rigid body rotation cooperative deformation model, the tunnel underpass scheme and the grouting ring setting scheme are evaluated according to the obtained vertical displacement of the tunnel, and the specific scheme can be designed and optimized by repeated adjustment of parameters and multiple times of substitution checking calculation.
Description
Technical Field
The invention belongs to the technical field of underground engineering, and particularly relates to a method for evaluating the protection effect of a grouting ring of a newly-built tunnel on an existing shield tunnel, which is suitable for a project for reinforcing the grouting ring arranged behind the newly-built tunnel wall, particularly for analyzing the protection effect of the grouting ring on the existing tunnel when a shield passes through the existing tunnel at a short distance.
Background
With the development of urban subway construction, more and more subway pipelines appear in a limited shallow stratum space, and the working condition that a newly-built shield tunnel passes through an existing tunnel at a short distance inevitably occurs. The close-distance crossing of the shield tunnel can cause the deformation of surrounding soil and the redistribution of soil stress, thereby affecting the structural safety of the existing tunnel, and certain protective measures need to be taken in the actual engineering to reduce the disturbance influence on the existing tunnel. The method is necessary to research the deformation rule of the existing tunnel and related measures for controlling deformation under the working condition of short-distance crossing of the shield.
Aiming at the problem that the shield passes through the existing tunnel in a short distance, the current main research methods comprise a numerical simulation method, an actual measurement data analysis method and a reduced size model test method. The accuracy of the numerical simulation method depends on the modeling level, the boundary conditions and the selection of parameters to a great extent, and the accuracy cannot be effectively guaranteed. The process of grouting in the tunnel to form the post-grouting ring relates to multiple action modes of permeation, compaction, splitting and the like of soil body slurry, influences the mechanism to be complex, the grouting ring is often combined with other control measures in actual engineering, the effects of different control measures are mutually superposed, and the effect of the grouting ring is difficult to be independently analyzed through an actual measurement data method. The reduced size model test cannot avoid the influence of the reduced size effect, is sensitive to disturbance of external factors, and cannot effectively guarantee accuracy. At present, no theoretical calculation method is available for carrying out independent analysis on the influence rule of the newly-built tunnel wall back grouting ring.
In summary, it is necessary to construct a mechanical model of the combined action of the newly-built tunnel, the grouting ring and the existing tunnel, and provide a calculation method considering the influence of the grouting ring of the newly-built tunnel on the vertical displacement of the existing tunnel.
Disclosure of Invention
The invention aims to provide a method for evaluating the protection effect of a newly-built tunnel grouting ring on an existing shield tunnel, and aims to solve the problems that the precision is difficult to control or single-factor analysis on the grouting ring cannot be realized in the calculation process by using the existing numerical simulation method, the actual measurement data analysis method and the reduced size model experiment method.
In order to achieve the above purpose, the technical solution adopted by the embodiment of the present invention is as follows:
a method for evaluating the protection effect of a grouting ring of a newly-built tunnel on an existing shield tunnel is characterized by comprising the following steps:
establishing a three-dimensional coordinate system according to the relative positions of a newly-built tunnel and an existing tunnel, arranging cutter additional thrust q at the front end of a shield body, arranging shield shell side frictional resistance f along the annular direction of the shield body, arranging additional grouting pressure p at the tail part of the shield body, and establishing a newly-built tunnel mechanical model;
according to the established new tunnel mechanical model, four factors of cutter additional thrust q, shield shell side frictional resistance f, additional grouting pressure p and soil body loss are considered, and the additional grouting pressure p is decomposed into vertical additional stress p 1 And horizontally additional stress p 2 Respectively calculating the additional stress generated by four factors at a certain point (x, y, z) on the axis of the existing tunnel along the vertical direction, and calculating to obtain the vertical additional stress sigma generated by q z-q F generated vertical additional stress sigma z-f 、p 1 Vertical additional stress sigma generated z-p1 、p 2 Vertical additional stress sigma generated z-p2 Additional stress sigma caused by soil loss z-s Summing the additional stresses to obtain the total vertical additional stress sigma at the axis of the existing tunnel caused by tunnel excavation z-k Adding stress sigma to the above-mentioned total vertical direction z-k On the basis of the stress of the vertical additional stress sigma at the axis of the existing tunnel caused by the grouting ring z-u The total vertical additional stress sigma borne by the existing tunnel can be obtained z ；
Calculating the vertical displacement of the existing tunnel through a shearing dislocation and rigid body rotation cooperative deformation model, and adding the final total vertical additional stress sigma z Substituting to obtain the final calculation formula of the vertical displacement omega of the existing tunnel, and substituting to any point in the calculation range to obtain the corresponding bitA set tunnel displacement value omega;
and evaluating according to the size of the obtained omega, and referring to the I-level control standard in the urban rail transit structure safety protection technical regulation, if the displacement value omega of the tunnel is less than 5mm, the tunnel is reasonable, otherwise, the tunnel is unreasonable.
According to the technical scheme, the embodiment of the invention has the beneficial effects that:
(1) the result obtained by the method is more consistent with the actually measured data, and the method can be used for calculating the vertical displacement value of the existing tunnel caused by the crossing of the newly built tunnel under the influence of the grouting ring.
(2) According to the method, the shearing and slab staggering deformation of the tunnel are considered in the calculation of the vertical deformation of the tunnel, and the calculation result is more accurate and is more consistent with the actual stress deformation mode of the tunnel structure.
(4) The method fully considers the calculation of the tunnel longitudinal displacement of the existing tunnel by the newly built tunnel grouting ring, and can truly reflect the influence of the newly built tunnel grouting ring on the tunnel vertical displacement.
(5) The method has certain accuracy in calculating the settlement value of the existing tunnel under the influence of the grouting ring of the newly-built tunnel, and can be used for analyzing the disturbance influence of the newly-built tunnel on the existing tunnel by adopting the grouting ring in the tunnel for reinforcement under the working condition of short-distance tunnel crossing.
Drawings
The accompanying drawings, which are included to provide a further understanding of the invention and are incorporated in and constitute a part of this specification, illustrate embodiments of the invention and together with the description serve to explain the invention and not to limit the invention. In the drawings:
FIG. 1 is a flow chart of a computing method provided by an embodiment of the invention;
FIGS. 2-4 are diagrams of computational models provided by embodiments of the present invention;
FIG. 5 is a diagram of a model for calculation of influence of grouting ring;
FIG. 6 is a volume expansion model of a grouting ring;
FIGS. 7-8 are graphs of the reliability verification of the calculation method provided by the embodiment of the present invention;
FIG. 9 is a graph showing the influence of the change in the volume expansion ratio Q on the additional stress of the existing tunnel in the example;
FIG. 10 is a graph showing the influence of the change in the volume expansion ratio Q on the vertical displacement of the existing tunnel in the embodiment;
FIG. 11 is a graph showing an influence of the length L of a grouting section on the additional stress of the existing tunnel in the embodiment;
FIG. 12 is a graph showing an influence of the length L of a grouting section on the vertical displacement of an existing tunnel in the embodiment;
FIG. 13 is a graph showing the effect of the change of the crossing angle α on the additional stress of the existing tunnel in the embodiment
Fig. 14 is a graph showing the influence of the change of the crossing angle α on the vertical displacement of the existing tunnel in the embodiment.
Description of reference numerals: newly building a tunnel 1; an existing tunnel 2; a cutting face 3; the ring 4 is grouted.
Detailed Description
The present invention will be further described with reference to the following examples. The following examples are set forth merely to aid in the understanding of the invention. It should be noted that, for those skilled in the art, it is possible to make various improvements and modifications to the present invention without departing from the principle of the present invention, and those improvements and modifications also fall within the scope of the claims of the present invention.
As shown in fig. 1, an embodiment of the present invention provides a method for calculating displacement of an existing tunnel under consideration of an influence of a newly-built tunnel grouting loop, including the following steps:
step S101, establishing a three-dimensional coordinate system according to the relative positions of the newly-built tunnel and the existing tunnel, and establishing a mechanical model: the front end of the shield body is provided with a cutter head additional thrust q, the circumferential direction of the shield body is provided with shield shell side frictional resistance f, and the tail part of the shield body is provided with additional grouting pressure p.
Step S102, respectively calculating additional stress along the vertical direction generated by four factors, namely cutter additional thrust q, shield shell side frictional resistance f, additional grouting pressure p and soil mass loss, at a certain point (x, y, z) at the axis of the existing tunnel according to the established mechanical model, and decomposing the additional grouting pressure p into vertical additional stress p for convenience of calculation 1 And horizontally attach toStress p 2 The vertical additional stress sigma generated by q can be obtained through calculation z-q F generated vertical additional stress sigma z-f 、p 1 Vertical additional stress sigma generated z-p1 、p 2 Vertical additional stress sigma generated z-p2 Additional stress sigma caused by soil loss z-s Finally, summing all the additional stresses to obtain the total vertical additional stress sigma at the axis of the existing tunnel caused by tunnel excavation z-k (ii) a Obtaining the vertical additional stress sigma at the axis of the existing tunnel caused by the grouting ring z-u Adding stress sigma to the above-mentioned total vertical direction z-k On the basis of which sigma is superimposed z-u The total vertical additional stress sigma borne by the existing tunnel can be obtained z 。
Step S103, calculating the vertical displacement of the existing tunnel by the shearing dislocation and rigid body rotation cooperative deformation model, and adding the final total vertical additional stress sigma z And substituting the final calculation formula to obtain the vertical displacement omega of the existing tunnel, and substituting any point in the calculation range to obtain the tunnel displacement value of the corresponding position.
And S104, evaluating according to the obtained magnitude of omega, referring to the I-level control standard in the urban rail transit structure safety protection technical regulation, and if the displacement value omega of the tunnel is less than 5mm, the displacement value is reasonable, otherwise, the displacement value is unreasonable.
Prior to the study, the following assumptions were first made: the foundation soil is assumed to be an isotropic, homogeneous, continuous, semi-infinite elastomer, and to extend indefinitely in both the depth and horizontal directions;
specifically, the step S101 specifically includes:
as shown in fig. 2-4, an x-axis is established on the ground along the axial direction of the newly-built tunnel, a y-axis is established perpendicular to the axial direction of the newly-built tunnel, and a z-axis is established vertically and downwards; the axis of the newly-built tunnel is located on the xoz plane, the upper part is an existing tunnel, the lower part is a newly-built tunnel, the two tunnels are overlapped up and down, the buried depth of the axis of the newly-built tunnel is H, the radius is R, the buried depth of the axis of the existing tunnel is H, and the radius is R s (ii) a The cutting surface at the front end of the newly-built tunnel is positioned at x ═ x 0 A cutter which is arranged on the cutting surface of the shield body and is forward along the x axisAnd (3) adding thrust q by a disc, setting shield shell side frictional resistance f along the circumferential direction of the shield body, and setting radial additional grouting pressure p at the tail part of the shield body to complete the construction of a newly-built tunnel mechanical model.
The above parameters are further explained as follows:
the x axis is along the shield tunneling direction, and the shield cutting surface is positioned at x ═ x 0 At m, the x coordinate is the horizontal distance from the shield cutting surface, and the unit symbol is m;
the y axis is horizontally vertical to the shield tunneling direction, the vertical projection of the central axis of the shield coincides with the x axis, the y coordinate is the horizontal distance from the shield axis, and the unit symbol is m;
the z axis is along the vertical direction, the z coordinate is the calculated depth below the earth surface, and the unit symbol is m;
p is additional grouting pressure of the shield tail, and the unit symbol is kPa;
f is the side frictional resistance of the shield shell, and the unit symbol is kPa;
q is additional thrust of the shield cutter head, and the unit symbol is kPa;
h and R are respectively the axial line buried depth and the radius of the shield at the newly-built tunnel, and the unit symbol is m;
h and R s Respectively the embedded depth and the radius of the existing tunnel axis, and the unit symbol is m;
specifically, step S102 specifically includes the following steps:
based on the Mindlin solution, the additional stress in the vertical direction generated by the additional thrust q of the cutter head, the side frictional resistance f of the shield shell and the additional grouting pressure p at a certain point (x, y, z) on the axis of the existing tunnel can be obtained.
2.1 q of vertical additional stress σ z-q
In the formula: r 1 And R 2 Are all the intermediate variables of the series of the Chinese characters,the specific relationship is
Mu is the Poisson's ratio of the soil; and r and theta are respectively the distance from the calculated point to the origin and the angle of the calculated point.
2.2 f resulting in a vertical additional stress σ z-f
In the formula: l is d The length of the shield machine; r 3 And R 4 Are all intermediate variables, the specific relationship is
s is an integral variable.
2.3 p resulting in a vertical additional stress σ z-p1 And σ z-p2
In the formula: m is a unit of 0 For tail grouting to influence length, R 5 And R 6 Are all intermediate variables, the specific relationship is
2.4 additional stress σ caused by soil loss z-s
Vertical displacement value U of soil body at any point of existing tunnel position caused by lower tunnel shield tunneling z ：
Wherein:
in the formula: B. lambda and delta are intermediate variables, k is the foundation bed coefficient, and
E 0 is the deformation modulus of soil, has
E s The compression modulus of foundation soil, b the width of a foundation beam, EI the equivalent bending rigidity of a tunnel, and mu the poisson ratio of a soil body; d is soil movementThe distance from the focus to the center point of the newly built tunnel; eta s The percentage (%) of the maximum soil loss, wherein eta (x) is a change function of the percentage of the soil loss along the x-axis direction;
further obtaining the additional stress sigma generated by the soil body loss at the axis of the existing tunnel z-s Comprises the following steps:
σ z-s ＝k·U z (10)
2.5 additional stress σ generated by slip casting Ring z-u
As shown in fig. 5 and 6, taking the 180 ° upper semicircular grouting ring as an example, the total length L of the grouting ring is L 1 +L 2 Wherein the yoz plane is taken as a boundary, L 1 And L 2 The lengths of the rear half section and the front half section of the grouting ring are respectively, the buried depth of the axis of the newly-built tunnel is H, and the radius of the newly-built tunnel is R. The buried depth of the newly-built tunnel axis is H, and the radius is R. And (3) selecting a calculating unit dV ═ d ζ d η in the grouting ring, wherein the buried depth of the calculating unit is η. The thickness of the grouting ring is t 1 Due to the influence of grouting, part of soil body in the original grouting area is extruded to form an edge expansion area, the thickness of the edge expansion area is delta t, and the thickness of the finally formed slurry-soil mixture is t 2 The volume expansion ratio is Q.
Integrating the grouting ring and the edge expansion area to obtain the vertical deformation U of the surrounding soil body caused by the post-grouting of the newly-built tunnel wall z-u And additional stress sigma z-u Comprises the following steps:
σ z-u ＝kU z-u (12)
in the formula: a. b is the integral upper and lower limits of a variable xi (along an x axis), c and d are the integral upper and lower limits of a variable zeta (along a y axis), e and f are the integral upper and lower limits of a variable eta (along a z axis), 1 in a subscript represents that an integral area is a grouting area, and 2 represents that the integral area is the grouting area and an edge expansion area; the calculation formula of the upper and lower limits of each integral is as follows: a is 1 ＝-L 1 、b 1 ＝L 2 、c 1 ＝-(R+t 1 )、d 1 ＝R+t 1 、
a 2 ＝-L 1 、b 2 ＝L 2 、c 2 ＝-(R+t 2 )、d 2 ＝R+t 2 、
Summing all the additional stresses to obtain the total vertical additional stress sigma at the axis of the existing tunnel caused by tunnel excavation z-k Adding stress sigma to the above-mentioned total vertical direction z-k On the basis of the stress of the vertical additional stress sigma at the axis of the existing tunnel caused by the grouting ring z-u The total vertical additional stress sigma borne by the existing tunnel can be obtained z 。
Specifically, the step S103 specifically includes the following steps:
under the influence of additional stress, relative corners and dislocation deformation can be generated between adjacent pipe sheets of the existing tunnel, the relative corners and dislocation deformation jointly cause total deformation of the tunnel in the longitudinal direction, and inter-ring tension and inter-ring shearing force can be generated between rings of each adjacent pipe sheet to resist deformation. From the analysis of the longitudinal deformation work doing and energy conversion angles of the tunnel, the additional stress generated by shield tunneling can be used for overcoming the resistance of the stratum, the shearing force between the segment rings and the pulling force between the rings to do work respectively. Namely, the following conditions are satisfied:
W σ ＝W R +W S +W T (13)
in the formula: w is a group of σ Acting total for additional stress, W R Acting to overcome formation resistance, W S To overcome the inter-ring shear force, W T Work is done to overcome the tension between the rings.
The respective work amount can be obtained by respectively integrating the additional stress, the formation resistance, the inter-ring shearing force and the inter-ring pulling force along the longitudinal direction of the tunnel.
In the formula: n is the number of the pipe piece rings on one side of the central point influenced by the additional stress on the existing tunnel, k s For tunnel inter-ring shear stiffness, k t Is the tensile rigidity between the tunnel rings, k is the foundation bed coefficient, j is the segment ring rigid body rotation effect proportionality coefficient, D t The ring width of each pipe piece is defined as m and m +1, the serial numbers of the adjacent two ring pipe piece rings are defined as D, the diameter of the existing tunnel is defined as w (l), the vertical displacement function of the existing tunnel is defined as w (l), and sigma (l) is a distribution function of total vertical additional stress along the axis of the existing tunnel; l is the length variation along the existing tunnel axis.
The vertical displacement function ω (l) of the shield tunnel is:
in the formula:
a is a matrix of undetermined coefficients in the displacement function, and is a ═ a 0 ,a 1 ···a n } T N is the expansion order of the Fourier series; n is the number of the affected segment rings on one side of the existing tunnel, D t The width of the ring of the pipe sheet is wide.
The calculation of each stress component in step S102 and the calculation of the vertical displacement of the existing tunnel in step S103 are both realized by Matlab, and a deformation curve of the existing tunnel along the longitudinal direction can be obtained, so that whether the bulging deformation of the existing tunnel is within the safety control range can be determined, and further, the design and safety verification of parameters such as an axis burial depth scheme of the newly-built tunnel, a scheme of a grouting ring of the newly-built tunnel, and the like can be performed.
On the basis of the step S104, design parameters and schemes can be optimized by repeatedly substituting, calculating and verifying tunnel crossing parameters and grouting ring design parameters, and the method has a certain meaning for guiding actual engineering design, and specifically includes the following steps:
evaluating according to the obtained omega size to determine the initial volume expansion rate Q 0 0 and a calculation accuracy Δ k;
when initial volume expansion rate Q 0 When the vertical displacement value is equal to 0, the vertical displacement value of the existing tunnel passing through the central point is obtained as omega 0 Less than 0; then taking a new volume expansion rate Q 1 ＝Q 0 + Δ k, Δ k is the calculation accuracy, using Q 1 The new vertical displacement value omega can be obtained 1 ；
If omega 1 If > 0, it means that the optimum volume expansion ratio is Q 0 -Q 1 If ω is 1 If less than 0, the new volume expansion rate Q needs to be continuously obtained 2 ＝Q 1 + Δ k, using Q 2 The new vertical displacement value omega can be obtained 2 ；
If omega 2 If > 0, it means that the optimum volume expansion ratio is Q 1 -Q 2 If ω is 1 If less than 0, the above process is continued, and Q is taken i+1 ＝Q i + Δ k (i ═ 2,3,4 … n) until we find a ω i+1 If the volume expansion ratio is more than 0, the operation can be stopped, and the optimal volume expansion ratio of the grouting ring is positioned at Q i -Q i+1 To (c) to (d);
get Q i -Q i+1 And calculating the vertical displacement value of the tunnel according to the volume expansion rate of the tunnel, and carrying out the next evaluation. Referring to the level I control standard in urban rail transit structure safety protection technical regulations, if the vertical displacement of the tunnel is less than 5mm, in the checking and calculating process, if the obtained maximum displacement value of the center of the tunnel is greater than 5mm, the design parameters need to be adjusted, and substitution, calculation and verification are carried out again. While countingThe calculated tunnel center displacement value meets the requirement of being less than 5mm, which shows that the design scheme is reasonable and has small influence on the existing tunnel.
Fig. 7 and 8 show graphs for verifying reliability of the calculation method according to the embodiment of the present invention. The existing double-line tunnel passing through the newly built tunnel in Hangzhou is taken as an engineering example. The newly-built tunnel is tunneled from right to left, an ascending line and a descending line of the existing tunnel are sequentially penetrated downwards, the downward penetrating angles are respectively 62 degrees and 61 degrees, in order to reduce the sedimentation influence of the downward penetrating of the tunnel on the existing double-line tunnel, after the shield penetrates through the existing line, the annular deep hole grouting can be carried out by adopting a steel pattern pipe within the influence range of the existing line, so that a semicircular grouting reinforcement ring is formed at the top of a 2021-2054-ring segment of the newly-built tunnel, the thickness of the grouting ring is 1.5m, the total reinforcement length L is 49.5m, and the newly-built tunnel and the existing tunnel are mainly located in a silt layer.
The main parameters needing to be input in the Matlab program calculation process comprise three blocks of soil parameters, shield related parameters and tunnel parameters.
1. Soil body parameters:
the Poisson ratio mu of the soil is 0.27; compression modulus E of foundation soil s 10.47 MPa; maximum soil mass loss rate eta caused by shield tunneling s ＝2％；
2. Shield related parameters:
the buried depth of the newly-built tunnel axis is 17.6 m; the radius of the shield is 3.35 m; the additional grouting pressure of the shield tail is p-120 kPa; the frictional resistance of the shield shell side is f-110 kPa; the additional thrust q of the shield cutter head is 45 kPa; the influence range of shield tail grouting is m 0 7.5 m; and d is 2.68m, the distance from the moving focus of the soil body to the center point of the newly-built tunnel. Length L of shield machine d ＝9m。
3. And (3) tunnel parameters:
the buried depth h of the existing tunnel axis is 11.0m on the uplink and 11.1m on the downlink; ring width of duct piece D t 1.5 m; radius of tunnel R s 6.2 m; the number of the selected lining ring rings with affected single side is N50; interannular shear stiffness k s ＝7.45×10 5 kN/m; tensile stiffness k between rings t ＝1.94×10 6 kN/m; equivalent tensile strength of tunnelEI＝1.1×10 8 kN·m 2 (ii) a The proportion j of the total sinking amount caused by the rotation of the rigid body is 0.3; the width b of the foundation beam is 6 m.
Get shield and construct excavation face and be located x 0 40m, and the volume expansion rate Q of the grouting ring is 1.58%. The settlement distribution curves of the existing tunnel of the ascending line are shown in comparison. As can be seen from fig. 7: (1) the tunnel settlement curve obtained by the calculation method is approximately in a normal distribution form, the actually measured settlement data is distributed in a mode of 'big middle and small two ends', and the overall distribution rules are the same; (2) the measured data and the tunnel maximum settlement value obtained by the calculation method are both positioned at the crossing central point and are respectively 3.2mm and 3.3mm, the difference value is only 0.1mm, and the accuracy requirement is met; (3) the tunnel settlement influence range obtained by the calculation method is closer to the actually measured data, and is approximately symmetrically distributed about the crossing center point. A comparison of the settlement profiles for the downline tunnels is shown. As can be seen from fig. 8: (1) the measured data shows that the settlement value of the tunnel near the crossing center is larger, the settlement values far away from the two sides of the crossing center are smaller, and the reflected settlement distribution rule is approximately consistent with the settlement curve obtained by the theoretical calculation method; (2) the measured value of the tunnel settlement near the crossing center point is slightly larger than the theoretical calculated value, for example, the measured value of the tunnel settlement near the crossing center point is 3.3mm, while the maximum value of the tunnel settlement obtained by the method is 3.15mm, and the difference is only 0.15mm, so that the accuracy requirement is met.
The calculation result obtained by the method is relatively consistent with the actually measured data, and the reliability of the evaluation method is proved. The calculation method has certain accuracy in calculating the settlement value of the existing tunnel under the influence of the grouting ring of the newly-built tunnel, can be used for analyzing the disturbance influence of the newly-built tunnel on the existing tunnel by adopting the grouting ring in the tunnel for reinforcement under the working condition of short-distance crossing of the tunnel, and has certain significance in guiding the actual engineering design.
As shown in fig. 9 and fig. 10, the influence curve of the change of the volume expansion ratio Q on the additional stress and the vertical displacement of the existing tunnel is shown, the working condition of the volume expansion ratio Q is divided into four kinds, and Q is 0%, Q is 1%, Q is 2%, and Q is 3%, as can be seen from fig. 4-1 and 4-2: (1) when Q is 0%, the additional stress curve borne by the existing tunnel meets normal distribution, and the maximum additional stress value passing through the center is 40.92 kPa; (2) along with the increase of Q, the acting force for lifting the existing tunnel at the upper part caused by the grouting ring is larger and larger, the total additional stress borne by the tunnel is gradually reduced, the curve of the additional stress gradually becomes gentle from downward projection to upward projection near the crossing center, and when Q is 3%, the additional stress borne by the existing tunnel is converted from downward projection to upward projection, which indicates that the influence of the grouting ring is larger than the influence generated by tunnel excavation; (3) the vertical displacement distribution curve of the tunnel under each working condition meets a normal distribution form, the maximum vertical displacement value occurs at the crossing central point, and when Q is respectively 0%, 1% and 2%, the maximum settlement value is 9.12mm, 5.35mm and 1.88mm in sequence; (4) the volume expansion influence of slip casting ring can effectively reduce the settlement deformation in the existing tunnel in upper portion, and along with the continuous increase of Q, the settlement of existing tunnel reduces gradually, and when Q equals 3%, the existing tunnel is become ascending uplift deformation by subsiding deformation conversion, and the biggest uplift volume in center is 2.16 mm. (5) According to the determination method of the optimal volume expansion rate of the grouting ring, the optimal expansion rate of the grouting ring of the engineering is between 2% and 3%.
Fig. 11 and 12 show the influence of the additional stress and the vertical displacement of the existing tunnel under different grouting length L working conditions. Fig. 11 and 12 are obtained by selecting and substituting parameters and calculating the Matlab program under the standard working condition of the case, and finally drawing. The case of the tunnel of the upper row line is taken as a standard working condition, and for the convenience of research, part of parameters are adjusted as follows: and alpha is 90 degrees, Q is 1 percent, L is 15m, 30m and 45m respectively are taken as research conditions, and other relevant parameters are kept unchanged. When passing through a single-line tunnel, the grouting sections are generally symmetrically arranged along the passing center point, so that L is provided 1 ＝L 2 0.5L. As can be seen from the figure: (1) when L is respectively 15m, 30m and 45m, the additional stress and the settlement value of the tunnel are gradually reduced, the maximum additional stress generated at the crossing central point is 26.77kPa, 24.47kPa and 23.68kPa in sequence, and the maximum settlement is 6.15mm, 5.35mm and 5.02mm in sequence; (2) the increase of the length of the grouting ring can reduce the settlement deformation of the upper existing tunnel, but the reduction amplitude is gradually reduced.
FIGS. 13 and 14 show an embodimentIn the example, the crossing angle alpha changes the additional stress and vertical displacement influence curve of the existing tunnel, the case of the tunnel of the upper row line is taken as a standard working condition, and for the convenience of research, part of parameters are adjusted as follows: l is a radical of an alcohol 1 ＝L 2 The study conditions are 15m and 1% for Q, 15 °, 30 °,45 °, 60 ° and 90 ° for α, respectively, and other relevant parameters are kept unchanged. As can be seen from fig. 13 and 14: (1) with the reduction of alpha, the maximum value of the additional stress borne by the center of the existing tunnel is almost unchanged and is about 25kPa, but the action range of the additional stress is continuously increased; (2) when alpha is more than or equal to 30 degrees, the additional stress curves are in normal distribution, when alpha is 15 degrees, the crossing angle of the new tunnel and the old tunnel is small, the influence length of the excavation and grouting ring on the existing tunnel is increased, the additional stress close to the crossing center is greatly influenced by the grouting ring, the section of curve becomes gentle, and the section of curve gradually bulges upwards along with the continuous reduction of alpha; (3) the additional stress curves are not symmetrically distributed along the crossing center, and the shield excavation surface is positioned at x in the study working condition 0 At the 40m position, the additional stress near the negative direction will be slightly greater than the additional stress in the positive direction; (4) the sedimentation amount of the existing tunnel is increased along with the reduction of alpha, when the alpha is respectively 90 degrees, 60 degrees, 45 degrees, 30 degrees and 15 degrees, the maximum sedimentation amount passing through the center is 5.35mm, 6.13mm, 7.26mm, 9.34mm and 13.14mm in sequence; (5) as α decreases, the existing tunnel settlement influence range will gradually increase.
The partial parameters related in the invention and the cited shearing dislocation and rigid body rotation deformation model are derived from a paper' Wei class, Shu-Ye, Yang wave, newly-built shield tunnel under-passing existing tunnel shearing dislocation deformation calculation [ J ]. Hunan university newspaper (natural science edition), 2018,45(9):103 + 112 and' Wei class, Zhang Xinhai, excavation of foundation pit causes rotation of lower horizontal shield tunnel and calculation of dislocation deformation [ J ]. school report of south-middle university: science version, 2019,50(9):2273 + 2284. "calculation of additional stress caused by soil loss part" article "Wei class. three-dimensional solution of soil deformation caused by shield tunnel construction [ C ]// second national engineering safety and protection academic conference and monograph set. Beijing: 2010: 369-.
The foregoing is only a preferred embodiment of the present invention, and it should be noted that, for those skilled in the art, various modifications and decorations can be made without departing from the principle of the present invention, and these modifications and decorations should also be regarded as the protection scope of the present invention.
Claims (7)
1. A method for evaluating the protection effect of a grouting ring of a newly-built tunnel on an existing shield tunnel is characterized by comprising the following steps:
establishing a three-dimensional coordinate system according to the relative positions of a newly-built tunnel and an existing tunnel, arranging cutter additional thrust q at the front end of a shield body, arranging shield shell side frictional resistance f along the annular direction of the shield body, arranging additional grouting pressure p at the tail part of the shield body, and establishing a newly-built tunnel mechanical model;
according to the established new tunnel mechanical model, four factors of cutter additional thrust q, shield shell side frictional resistance f, additional grouting pressure p and soil mass loss are considered, and the additional grouting pressure p is decomposed into vertical additional stress p 1 And horizontally additional stress p 2 Respectively calculating the additional stress generated by four factors at a certain point (x, y, z) on the axis of the existing tunnel along the vertical direction, and calculating to obtain the vertical additional stress sigma generated by q z-q F generated vertical additional stress sigma z-f 、p 1 Vertical additional stress sigma generated z-p1 、p 2 Vertical additional stress sigma generated z-p2 Additional stress sigma caused by soil loss z-s Summing the additional stresses to obtain the total vertical additional stress sigma at the axis of the existing tunnel caused by tunnel excavation z-k Adding stress sigma to the above-mentioned total vertical direction z-k On the basis of the stress of the vertical additional stress sigma at the axis of the existing tunnel caused by the grouting ring z-u The total vertical additional stress sigma borne by the existing tunnel can be obtained z ；
Calculating the vertical displacement of the existing tunnel through a shearing dislocation and rigid body rotation cooperative deformation model, and adding the final total vertical additional stress sigma z Substituting the final calculation formula to obtain the vertical displacement omega of the existing tunnel, and substituting the final calculation formula to any point in the calculation rangeObtaining a tunnel displacement value omega of a corresponding position;
evaluating according to the size of the obtained omega, referring to the I-level control standard in urban rail transit structure safety protection technical rules, if the displacement value omega of the tunnel is less than 5mm, the tunnel is reasonable, otherwise, the tunnel is unreasonable;
wherein, the vertical additional stress sigma at the axis of the existing tunnel caused by the grouting ring z-u The calculation process of (2) is as follows:
the total length L of the semicircular grouting ring on the newly-built tunnel is equal to L 1 +L 2 The buried depth of the axis of the newly-built tunnel is H, and the radius of the newly-built tunnel is R; a calculation unit dV ═ d ξ d ζ d η is arbitrarily selected in the grouting ring, and the buried depth of the calculation unit is η; the thickness of the grouting ring is t 1 Due to the influence of grouting, part of soil body in the original grouting area is extruded to form an edge expansion area, the thickness of the edge expansion area is delta t, and the thickness of the finally formed slurry-soil mixture is t 2 The volume expansion rate is Q;
integrating the grouting ring and the edge expansion area to obtain the vertical deformation U of the surrounding soil body caused by the post-grouting of the newly-built tunnel wall z-u And additional stress sigma z-u Comprises the following steps:
σ z-u ＝kU z-u (12)
in the formula: a. b is the upper and lower limits of the integral of the variable xi along the x axis, c and d are the upper and lower limits of the integral of the variable zeta along the y axis, e and f are the upper and lower limits of the integral of the variable eta along the z axis, 1 in the subscript represents that the integral area is a grouting area, and 2 represents that the integral area is a grouting area and an edge expansion area; the calculation formula of the upper and lower limits of each integral is as follows: a is 1 ＝-L 1 、b 1 ＝L 2 、c 1 ＝-(R+t 1 )、d 1 ＝R+t 1 、
a 2 ＝-L 1 、b 2 ＝L 2 、c 2 ＝-(R+t 2 )、d 2 ＝R+t 2 、
2. The method for evaluating the protection effect of the grouting ring of the newly-built tunnel on the existing shield tunnel according to claim 1, wherein the establishment of a mechanical model of the newly-built tunnel specifically comprises the following steps:
establishing an x axis along the axis direction of the newly-built tunnel on the ground, establishing a y axis vertical to the axis direction of the newly-built tunnel, and establishing a z axis vertically downwards; the axis of the newly-built tunnel is located on the xoz plane, the upper part is an existing tunnel, the lower part is a newly-built tunnel, the two tunnels are overlapped up and down, the buried depth of the axis of the newly-built tunnel is H, the radius is R, the buried depth of the axis of the existing tunnel is H, and the radius is R s (ii) a The cutting surface at the front end of the newly-built tunnel is positioned at x ═ x 0 And arranging cutter head additional thrust q along the positive direction of the x axis on the cutting surface of the shield body, arranging shield shell side frictional resistance f along the annular direction of the shield body, and arranging radial additional grouting pressure p at the tail part of the shield body to complete the construction of a newly-built tunnel mechanical model.
3. The method for evaluating the protective effect of the grouting ring of the newly-built tunnel on the existing shield tunnel according to claim 2, wherein the vertical additional stress sigma generated by q is z-q The calculation process is as follows:
in the formula: r 1 And R 2 Are all intermediate variables, the specific relationship is
Mu is the Poisson's ratio of the soil; and r and theta are respectively the distance from the calculated point to the origin and the angle of the calculated point.
4. The method for evaluating the protective effect of the grouting ring of the newly-built tunnel on the existing shield tunnel according to claim 1, wherein f generates vertical additional stress sigma z-f The calculation process is as follows:
in the formula: l is d The length of the shield machine; r 3 And R 4 Are all intermediate variables, the specific relationship is
s is an integral variable.
5. The method for evaluating the protective effect of the grouting ring of the newly-built tunnel on the existing shield tunnel according to claim 1, wherein p generates vertical additional stress sigma z-p1 And additional stress sigma in the horizontal direction z-p2 The calculation process is as follows:
in the formula: m is a unit of 0 For tail grouting to influence length, R 5 And R 6 Are all intermediate variables, the specific relationship is
6. The method for evaluating the protective effect of the grouting ring of the newly-built tunnel on the existing shield tunnel according to claim 1, wherein the additional stress sigma caused by soil loss z-s The calculation process is as follows:
vertical displacement value U of soil body at any point of existing tunnel position caused by shield tunneling z ：
Wherein:
in the formula: B. lambda and delta are intermediate variables, k is the foundation bed coefficient, and
E 0 is the deformation modulus of soil, has
E s The compression modulus of foundation soil, b the width of a foundation beam, EI the equivalent bending rigidity of a tunnel, and mu the poisson ratio of a soil body; d is the distance from the moving focus of the soil body to the center point of the newly-built tunnel; eta s The percentage (%) of the maximum soil loss, wherein eta (x) is a change function of the percentage of the soil loss along the x-axis direction;
further obtaining the additional stress sigma generated by the soil body loss at the axis of the existing tunnel z-s Comprises the following steps:
σ z-s ＝k·U z (10)。
7. the method for evaluating the protection effect of the grouting ring of the newly-built tunnel on the existing shield tunnel according to claim 1, wherein the process of calculating the vertical displacement of the existing tunnel through the shearing dislocation and rigid rotation cooperative deformation model is as follows:
the additional stress generated by shield tunneling can be used for overcoming the resistance of the stratum, the shearing force between the segment rings and the tension between the rings to respectively do work, and the requirements are met:
W σ ＝W R +W S +W T (13)
in the formula: w σ Acting total for additional stress, W R Acting to overcome formation resistance, W S To overcome the inter-ring shear force, W T In order to overcome the tension between the rings to do work, wherein,
in the formula: n is the number of the pipe piece rings on the single side of the central point influenced by the additional stress on the existing tunnel, k s For tunnel inter-ring shear stiffness, k t Is the tensile rigidity between the tunnel rings, k is the foundation bed coefficient, j is the segment ring rigid body rotation effect proportionality coefficient, D t The ring width of each pipe piece is defined as m and m +1, the serial numbers of the adjacent two ring pipe piece rings are defined as D, the diameter of the existing tunnel is defined as w (l), the vertical displacement function of the existing tunnel is defined as w (l), and sigma (l) is a distribution function of total vertical additional stress along the axis of the existing tunnel; l is the length variable along the axial direction of the existing tunnel;
the vertical displacement function ω (l) of the shield tunnel is:
in the formula:
a is a matrix of undetermined coefficients in the displacement function, and is a ═ a 0 ,a 1 ···a n } T N is the expansion order of the Fourier series; n is the number of the affected segment rings on one side of the existing tunnel, D t The width of the ring of the pipe sheet is wide.
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